利用自相似性量化宇宙学N体模拟的分辨率
Quantifying resolution in cosmological N-body simulations using self-similarity
摘要：
我们证明，在无标度模拟的自相似性测试提供了一个很好的工具，以量化的分辨率在小尺度的宇宙学N体模拟。分析两点关联函数测量模拟使用ABACUS，我们展示了如何观察到的自相似性的偏差揭示了收敛的时间和距离尺度的范围。虽然收敛良好的尺度显示精度低于1%，但我们的结果表明，在较小的力软化长度下，空间分辨率基本上取决于质量分辨率。在以后的时间里，收敛的下限截止尺度在共动单位中演变为$a^{-1/2}$（$a$是尺度因子），这与它是由两体碰撞性设定的假设一致。我们的研究结果的一个推论是，N体模拟，特别是在高红移，包含一个显着的空间范围内，集群出现收敛的时间步长和力软化，但实际上并没有收敛到物理连续的结果。开发的方法可以应用于确定任何聚类统计的分辨率，并扩展到推断非无标度模拟的分辨率限制。
英文摘要：
We demonstrate that testing for self-similarity in scale-free simulations provides an excellent tool to quantify the resolution at small scales of cosmological N-body simulations. Analysing two-point correlation functions measured in simulations using ABACUS, we show how observed deviations from self-similarity reveal the range of time and distance scales in which convergence is obtained. While the well-converged scales show accuracy below 1 percent, our results show that, with a small force softening length, the spatial resolution is essentially determined by the mass resolution. At later times the lower cut-off scale on convergence evolves in comoving units as $a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it is set by two-body collisionality. A corollary of our results is that N-body simulations, particularly at high red-shift, contain a significant spatial range in which clustering appears converged with respect to the time-stepping and force softening but has not actually converged to the physical continuum result. The method developed can be applied to determine the resolution of any clustering statistic and extended to infer resolution limits for non-scale-free simulations.
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